# solvable group

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## solvable group

[′säl·və·bəl ′grüp]
(mathematics)
A group G which has subgroups G0, G1,…, Gn , where G0= G, Gn = the identity element alone, and each Gi is a normal subgroup of Gi-1with the quotient group Gi-1/ Gi Abelian.
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A solvable group has a subnormal series of subgroups.
by [5], A5 is the smallest non abelian simple group of order 22 .3.5 and the smallest non solvable group containing four conjugacy classes.
[Abels:1971] Abels Herbert, 1971, An example of a finitely presented solvable group, London Mathematical Society lecture notes, Cambridge: Cambridge University Press, pp.
any closed, undistorted subgroup (e.g., cocompact lattice) of a direct product of a p-adic solvable group with a connected, solvable Lie group.
Tessera, see Theorem 4.3 shows that there exists a solvable group [GAMMA] such that W([GAMMA]) contains S[L.sub.3](Z).
A long standing open problem in the character theory of finite solvable groups is whether the derived length dl(G) of a solvable group G is bounded above by the cardinality of cd(G), the set of irreducible character degrees of that group, i.e.
We begin by proving that the generalized free product of a nilpotent group and a solvable group is not necessarily perfect.
Here we recall that every binary solvable group except [Q.sub.8] (the group of quaternions) has been proved to be symmetrically sequenceable in [2].
And for a general connected solvable group S, the Lie subalgebra t [intersection] [s, s] is always central in s.
Let G be a solvable group in which [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], for 1 [less than or equal to] [[alpha].sub.1] [less than or equal to] [[alpha].sub.2], p a prime and [absolute value of G:C] a prime.
Let G be a solvable group, then one of the following holds.
One may extend the definition of isotropic torus to the case of solvable groups as follows.

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